mlsanityData to 7 Oct 2026

PINNup: Robust neural network wavefield solutions using frequency upscaling and neuron splitting

arXiv 2109.14536 ↗First posted 29 Sep 2021cs.LG physics.comp-phcited by 20

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Abstract (arXiv)

Solving for the frequency-domain scattered wavefield via physics-informed neural network (PINN) has great potential in seismic modeling and inversion. However, when dealing with high-frequency wavefields, its accuracy and training cost limits its applications. Thus, we propose a novel implementation of PINN using frequency upscaling and neuron splitting, which allows the neural network model to grow in size as we increase the frequency while leveraging the information from the pre-trained model for lower-frequency wavefields, resulting in fast convergence to high-accuracy solutions. Numerical results show that, compared to the commonly used PINN with random initialization, the proposed PINN exhibits notable superiority in terms of convergence and accuracy and can achieve neuron based high-frequency wavefield solutions with a two-hidden-layer model.

Key facts. Cited by 20 papers in the map (data through 7 Oct 2026). Builds on 4 of its 17 references that are in the map. First posted on arXiv 29 Sep 2021.

Builds on

4 of 17 references.

References · 4

  1. 2020Implicit Neural Representations with Periodic Activation Functionscited by 2,214
  2. 2014Breaking the Curse of Dimensionality with Convex Neural Networkscited by 329
  3. 2015Net2Net: Accelerating Learning via Knowledge Transfercited by 245
  4. 2019Splitting Steepest Descent for Growing Neural Architecturescited by 52

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 2; 2023: 10; 2024: 0; 2025: 6; 2026: 2.

20 papers.

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  1. 2022Implicit Full Waveform Inversion with Deep Neural Representationcited by 26
  2. 2022Incremental Spatial and Spectral Learning of Neural Operators for Solving Large-Scale PDEscited by 25
  3. 2023Efficient physics-informed neural networks using hash encodingcited by 21
  4. 2023InRank: Incremental Low-Rank Learningcited by 10
  5. 2023GaborPINN: Efficient physics informed neural networks using multiplicative filtered networkscited by 7
  6. 2023Microseismic source imaging using physics-informed neural networks with hard constraintscited by 5
  7. 2023LatentPINNs: Generative physics-informed neural networks via a latent representation learningcited by 5
  8. 2023Physics-informed neural wavefields with Gabor basis functionscited by 5
  9. 2025Physics-informed waveform inversion using pretrained wavefield neural operatorscited by 5
  10. 2025RED-DiffEq: Regularization by denoising diffusion models for solving inverse PDE problems with application to full waveform inversioncited by 5
  11. 2023A Critical Review of Physics-Informed Machine Learning Applications in Subsurface Energy Systemscited by 4
  12. 2025Neuro-Spectral Architectures for Causal Physics-Informed Networkscited by 3
8 more
  1. 2023Physics-informed neural network for seismic wave inversion in layered semi-infinite domaincited by 2
  2. 2025An effective physics-informed neural operator framework for predicting wavefieldscited by 2
  3. 2023PINNslope: seismic data interpolation and local slope estimation with physics informed neural networkscited by 1
  4. 2025DiffPINN: Generative diffusion-initialized physics-informed neural networks for accelerating seismic wavefield representationcited by 1
  5. 2026Enforcing Reciprocity in Operator Learning for Seismic Wave Propagationcited by 1
  6. 2023Overview of Physics-Informed Machine Learning Inversion of Geophysical Datacited by 0
  7. 2025PreAdaptFWI: Pretrained-Based Adaptive Residual Learning for Full-Waveform Inversion Without Dataset Dependencycited by 0
  8. 2026Staged Depth Training: A Representation Curriculum for PINNscited by 0